Computation of moment generating and characteristic functions with Mathematica

Date of Defense

2003-05-30

Page Count

11

Keyword

characteristic function

moment generating function

law of large numbers

computer algebra system

Mathematica

central limit theorem

Abstract

Mathematica is an extremely powerful and flexible symboliccomputer algebra system that enables the user to deal withcomplicated algebraic tasks. It can also easily handle thenumerical and graphical sides. One such task is the derivation ofmoment generating functions (MGF) and characteristic functions(CF), demonstrably effective tools to characterize a distribution.In this paper, we define some rules in Mathematica to help incomputing the MGF and CF for linear combination of independentrandom variables. These commands utilizes pattern-matching codethat enhances Mathematica's ability to simplify expressionsinvolving the product of algebraic terms. This enhancement toMathematica's functionality can be of particular benefit for MGFand CF. Applications of these rules to determine mean, varianceand distribution are illustrated for various independent randomvariables.